Free group

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Free group: A group freely generated by a set. The elements of the group are simply words whose letters are elements of the set and their inverses, with multiplication of words being by concatenation, and where the only rules for simplifying words are the cancellation of an element and its inverse when placed adjacent to each other.

Primary subject wiki entry: Groupprops:Free group

Also located at: Wikipedia:Free group, Mathworld:FreeGroup, Planetmath:FreeGroup